So help me understand. Adding a amplifier for the LCR will not have any noticeable impact until volume reaches levels the AVR would normally cut off?
Your question can be difficult to answer clearly because the differences from a larger amp can be subtle and hard to easily describe in words. A number of years ago I added an external 200 wpc amp to my existing AVR. The 2 channel amp drove my front L and R speakers. The AVR was a modest Denon rated at 70 wpc. So the power increase was about triple.
At first I couldn't say I noticed anything had changed. But soon I noticed that the speaker's bass seemed a little more crisp and firm (less bloated?) on certain musical selections. It was subtle, and depended on the music, so it wasn't always noticeable. Within a few weeks I started noticing that the cues for sound that was comfortably loud and too loud had changed. I could listen at louder levels without noticing that it was uncomfortably loud. After that, I started turning it down.
Apparently, with the AVR I had judged when to turn it down by the amount of noise or distortion I was hearing. When I started using the bigger amp, those cues were less noticeable. It's not unlike driving a car, where I could estimate my speed by listening to the road noise. If I got new tires, or drove on smoother pavement, those cues changed and my sense of speed was wrong. The more powerful amp was apparently quieter, as in less noisy than the smaller amp, while at the same time, driving the speakers louder.
I hope that makes sense.